Question 230586
The difference of two numbers is 16. The larger number is 4 less than 3 times the smaller. Find the two numbers


Step 1.  Let x be one and smaller number.


Step 2.  Let 3x be three times the smaller number.


Step 3.  Let x+16 be the other number since their difference is 16.


Step 4.  Then x+16=3x-4 since since the larger number is 4 less than 3 times the smaller.


Step 5.  Solving x+16=3x-4 leads to the following steps.


Add 4-x to both sides of the equation to get only x terms on one side and only numbers on the other side.


{{{x+16+4-x=3x-4+4-x}}}


{{{20=2x}}}


Divide by 2 to both sides to find x


{{{20/2=2x/2}}}


{{{x=10}}} and {{{16+10=26}}}


Check if larger number is 4 less than three times the smaller.  


{{{26=3*10-4}}}


{{{26=26}}} which is a true statement


Step 6.  ANSWER:  The numbers are 10 and 26.